Shahen Nur Hasan Mahmud, Al Amin Md, Rahman M M
Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, 1000, Bangladesh.
Department of Arts and Sciences, Bangladesh Army University of Science and Technology, Saidpur, 5310, Bangladesh.
Sci Rep. 2024 Jul 16;14(1):16420. doi: 10.1038/s41598-024-61405-8.
This study retrieves some novel exact solutions to the family of 3D space-time fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) equations in the context of diverse nonlinear physical phenomena resulting from water wave mechanics. The family of WBBM equations is transformed for this purpose using a space and time fractional transformation into an ordinary differential equation (ODE). The ODE then uses a strong method, namely the Unified Method. Consequently, lump solutions, dark-bright soliton, singular and multiple soliton solutions, and periodic solutions are investigated. The disparities between the current study's conclusions and previously acquired solutions via other approaches are examined. All wave solutions produced are determined to be novel in terms of fractionality, unrestricted parameters, and implemented technique sense. The impact of unrestricted parameters and fractionality on the obtained solutions are visually presented, along with physical explanations. It is observed that the wave portents are varied with the increase of unrestricted parameters as well as fractionality. We dynamically showed that the appropriate transformation and the applied Unified approach more proficient in the study of water wave dynamics and might be used in future researches to clarify the many physical phenomena. The novelty of this work validate that the proposed method seem simple and useful tools for obtaining the solutions in PDEs and it is expected to use in mathematical physics and optical engineering.
本研究在水波力学所产生的各种非线性物理现象的背景下，获取了三维时空分数阶瓦兹瓦兹 - 本杰明 - 博纳 - 马奥尼（WBBM）方程族的一些新颖精确解。为此，利用时空分数变换将WBBM方程族转化为一个常微分方程（ODE）。然后，该ODE采用一种强大的方法，即统一方法。因此，研究了块状解、暗 - 亮孤子、奇异和多重孤子解以及周期解。研究了本研究结论与先前通过其他方法获得的解之间的差异。所产生的所有波解在分数阶、无限制参数和所采用技术意义方面均被确定为新颖的。直观地展示了无限制参数和分数阶对所得解的影响，并给出了物理解释。可以观察到，波的特征随着无限制参数以及分数阶的增加而变化。我们动态地表明，适当的变换和所应用的统一方法在水波动力学研究中更有效，并且可能用于未来的研究以阐明许多物理现象。这项工作的新颖性验证了所提出的方法似乎是用于获得偏微分方程解的简单而有用的工具，并且有望应用于数学物理和光学工程。
